Quantum Littlewood-Richarson Coefficients and Harish-Chandra Induction for Finite General Linear Groups

有限一般线性群的量子Littlewood-Richarson系数和Harish-Chandra归纳

• 批准号: 9900134
• 负责人: Alexander Kleshchev
• 金额: $ 7.5万
• 依托单位: University of Oregon Eugene
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-06-15 至 2002-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9900134&HistoricalAwards=false
• 关键词: Quantum; Littlewood; Richarson; Coefficients; Harish

9900134This project is concerned with the branching rules for quantum linear groups and their applications to the modular representation theory of finite groups. The PI will study irreducible restrictions of irreducible modules of the symmetric group to its subgroups. This problem is crucial for describing the subgroup structure in finite simple groups. Other applications include the combinatorics of the Fock space, an object important in mathematical physics. We also study the two-sided ideal structure of group algebras of some locally finite groups, the combinatorics of partitions, partition identities, symmetric functions, Hecke algebras, and other topics in combinatorics.The main area of research in this proposal is group theory and the representation theory of symmetric groups. The symmetric group consists of all permutations of a finite set. It is one of the central objects in mathematics, and is extremely important for applications to physics and chemistry. Recent results demonstrate a strong connection between some representations of the symmetric group and certain restricted solid-on-solid models.

9900134这个项目与量子线性群体的分支规则及其在有限群体的模块化表示理论中的应用有关。 PI将研究对称群体对其亚组的不可还原模块的不可还原限制。此问题对于描述有限简单组中的亚组结构至关重要。 其他应用程序包括Fock空间的组合，这在数学物理学中很重要。 我们还研究了一些本地有限群体的组代数的双面理想结构，分区的组合，分区身份，对称函数，Hecke代数和组合学中的其他主题。 对称组由有限集的所有排列组成。它是数学中的中心对象之一，对于物理和化学的应用非常重要。 最近的结果表明，对称组的某些表示与某些受限的固体固体模型之间存在密切的联系。